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From: A.P. Palling on 2 Apr 2010 20:53

http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/1
1703.html?type=print


(10^15 + 7.2 - 10^15)* 100 = 0

(10^15 - 10^15 + 7.2)* 100 = 720


etc.

From: Virgil on 2 Apr 2010 21:50
In article <4bb69192$0$24265$c3e8da3(a)news.astraweb.com>,
"A.P. Palling" <Ono_Snoino(a)ono.ono> wrote:

> http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/1
> 1703.html?type=print
>
>
> (10^15 + 7.2 - 10^15)* 100 = 0
>
> (10^15 - 10^15 + 7.2)* 100 = 720
>
>
> etc.

But in exact mode,
(10^15 + 36/5 - 10^15)*100 = (10^15 - 10^15 + 36/5)*100 = 720

In floating point calculations, i.e., in your set of calculations, one
expects certain errors due to roundoff. These will occur when adding or
subtracting numbers whose most significant digits occur at widely
different place values.
From: A.P. Palling on 3 Apr 2010 13:23
Virgil <Virgil(a)home.esc> wrote in
news:Virgil-0C3F71.19505602042010(a)bignews.usenetmonster.com:

> In article <4bb69192$0$24265$c3e8da3(a)news.astraweb.com>,
> "A.P. Palling" <Ono_Snoino(a)ono.ono> wrote:
>
>> http://apcentral.collegeboard.com/apc/members/courses/teachers_cor
>> ner/1 1703.html?type=print
>>
>>
>> (10^15 + 7.2 - 10^15)* 100 = 0
>>
>> (10^15 - 10^15 + 7.2)* 100 = 720
>>
>>
>> etc.
>
> But in exact mode,
> (10^15 + 36/5 - 10^15)*100 = (10^15 - 10^15 + 36/5)*100 = 720
>
> In floating point calculations, i.e., in your set of calculations,
> one expects certain errors due to roundoff. These will occur when
> adding or subtracting numbers whose most significant digits occur
> at widely different place values.

I love the idea of bamboozling the equipment.
I've a warped sense of humor, I suppose.

True, Exact relies on no fixed value, and approximate
is the most exact possible (given the hardware and algorhythms).

A sphere's cross section is perfectly happy to exist
despite our inability to express it precisely
by the 10-finger method.

Hey, do primes exist in the same places using different bases?
(chuckle.)

From: Tom Lake on 9 Apr 2010 05:28

"A.P. Palling" <Ono_Snoino(a)ono.ono> wrote in message
news:4bb69192$0$24265$c3e8da3(a)news.astraweb.com...
>
> http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/1
> 1703.html?type=print
>
>
> (10^15 + 7.2 - 10^15)* 100 = 0
>
> (10^15 - 10^15 + 7.2)* 100 = 720
>

I don't see the problem there.

Adding 7.2 to 10^15 can still give 10^15 when there are a finite
number of significant digits. With most computers, I'd expect 0 in this
case.
When you subtract 10^15 from 10^15 you get 0 and adding 7.2
to that gives 7.2, which multiplied by 100 gives 720, again,
just as expected. Maybe I've just been working with floating-point
too long....

Tom Lake

From: Han on 9 Apr 2010 16:43
On Apr 9, 5:28 am, "Tom Lake" <tl...(a)twcny.rr.com> wrote:
> "A.P. Palling" <Ono_Sno...(a)ono.ono> wrote in message
>
> news:4bb69192$0$24265$c3e8da3(a)news.astraweb.com...
>
>
>
> >http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/1
> > 1703.html?type=print
>
> > (10^15 + 7.2 - 10^15)* 100  = 0
>
> > (10^15 - 10^15 + 7.2)* 100  = 720
>
> I don't see the problem there.
>
> Adding 7.2 to 10^15 can still give 10^15 when there are a finite
> number of significant digits.  With most computers, I'd expect 0 in this
> case.
> When you subtract 10^15 from 10^15 you get 0 and adding 7.2
> to that gives 7.2, which multiplied by 100 gives 720, again,
> just as expected.  Maybe I've just been working with floating-point
> too long....
>
> Tom Lake

I think the point was that there are students who "don't think" about
such details and are clueless as to why when they obtain unexpected
answers.
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